Progressive addition lenses with reduced unwanted astigmatism

ABSTRACT

The invention provides lenses in which the maximum unwanted astigmatism is reduced and distributed over a wide area.

FIELD OF THE INVENTION

The present invention relates to multifocal ophthalmic lenses. Inparticular, the invention provides progressive addition lens designs,and lenses in which unwanted astigmatism is reduced, which lenses aresubstantially free of localized unwanted astigmatism maxima. Thisapplication is a continuation of application Ser. No. 10/870,114 whichis a continuation-in-part of co-pending application Ser. No. 10/726,735which is a divisional of application Ser. No. 09/832,236 issued as U.S.Pat. No. 6,709,105.

Background of the Invention

The use of ophthalmic lenses for the correction of ametropia is wellknown. For example, multifocal lenses, such as progressive additionlenses (“PALs”) are used for the treatment of presbyopia. Theprogressive surface of a PAL provides far, intermediate, and near visionin a gradual, continuous progression of vertically increasing dioptricpower from far to near focus, or top to bottom, of the lens.

PALs are appealing to the wearer because PALs are free of the visibleledges between the zones of differing dioptric power that are found inother multifocal lenses, such as bifocals and trifocals. However, aninherent disadvantage of PALs is the presence of unwanted astigmatism,or astigmatism that is undesirable and is introduced or caused by one ormore of the lens' surfaces. Unwanted astigmatism can produce swim, imagemagnification, and motion effects for the lens wearer that disrupts thewearer's vision. In hard PAL lens designs, the unwanted astigmatismborders the lens channel and near vision zone. In soft designs, theunwanted astigmatism may extend into the distance zone. Generally, inboth designs, the unwanted astigmatism at or near its approximate centerreaches a maximum that corresponds approximately to the near visiondioptric power of the lens. A need exists for lens designs in whichthese localized maxima are reduced or substantially eliminated.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 a is a contour map of the unwanted astigmatism of a first priorart progressive lens.

FIG. 1 b is a power and cylinder contour profile of the lens of FIG. 1a.

FIG. 2 a is a contour map of the unwanted astigmatism of a second priorart progressive lens.

FIG. 2 b is a power and cylinder contour profile of the lens of FIG. 2a.

FIG. 3 a is a contour map of the unwanted astigmatism of a third priorart progressive lens.

FIG. 3 b is a power and cylinder contour profile of the lens of FIG. 3a.

FIG. 4 a is a contour map of the unwanted astigmatism of a surface of alens of the invention.

FIG. 4 b is a power and cylinder contour profile of the lens of FIG. 4a.

FIG. 5 a is a contour map of the unwanted astigmatism of a secondsurface of a lens of the invention.

FIG. 5 b is a power and cylinder contour profile of the lens of FIG. 5a.

DESCRIPTION OF THE INVENTION AND ITS PREFERRED EMBODIMENTS

The present invention provides lenses, and methods for their design andmanufacture, in which the maximum unwanted astigmatism is reduced anddistributed over a wide area. The lenses of the invention are providedby locally manipulating sag values of a progressive surface.

In one embodiment, the invention provides a method for designing aprogressive addition lens, comprising, consisting essentially of, andconsisting of: a.) designing a first progressive addition surface havinga channel and one or more

areas of unwanted astigmatism on either side of the channel, each areaof unwanted astigmatism comprising a maximum unwanted astigmatism; b.)expressing the first surface as a plurality of sag values; and c.)modifying each of the one or more areas of unwanted astigmatism toprovide a second progressive addition surface in which the maximumunwanted astigmatism of each of the areas is reduced and the unwantedastigmatism is substantially constant within each of the areas. Inanother embodiment, the invention provides lenses made according to thismethod.

By “lens” is meant any ophthalmic lens including, without limitation,spectacle, contact, intraocular lenses and the like. Preferably, thelens of the invention is a spectacle lens. By “sag value” is meant theabsolute value of the z axis distance between a point on a progressivesurface located at coordinates (x, y) and a corresponding point on areference plane. For purposes of the invention, the z axis is the axisorthogonal to the x-y plane.

By “progressive addition surface” or “progressive surface” is meant acontinuous, aspheric surface having distance and near viewing zones, anda zone of increasing dioptric power connecting the distance and nearzones. One ordinarily skilled in the art will recognize that, if theprogressive surface is the convex surface of the lens, the distancevision zone curvature will be less than that of the near zone curvatureand if the progressive surface is the lens' concave surface, thedistance curvature will be greater than that of the near zone.

By “channel” is meant the corridor of vision that is free of unwantedastigmatism of about 0.75, preferably about 1.00, diopters or greaterwhen the wearer's eye is scanning through the intermediate vision zoneto the near vision zone and back.

By “unwanted astigmatism” is meant astigmatism that is undesirable andis introduced or caused by the lens surface. For purposes of theinvention, the areas of

unwanted astigmatism considered are those located on either side of thechannel and preferably below the fitting point. By “fitting point” ismeant is the point on a lens aligned with the wearer's pupil in itsdistance viewing position when the wearer is looking straight ahead.

In the first step of the method of the invention, a first progressivesurface is provided by any convenient optical design method. Thissurface, u(x, y), may be a single progressive surface or a surface thatis the result of combining one or more progressive and regressivesurfaces. By “regressive surface” is meant a continuous, asphericsurface having zones of distance and near vision and a zone ofdecreasing dioptric power connecting the distance and near zones. If theregressive surface is the convex surface of the lens, the distance zonecurvature will be greater than that of the near zone and if theregressive surface is the lens' concave surface. The distance curvaturewill be less than that of the near zone.

Designing of the first progressive surface u(x, y) preferably is carriedout using a method that divides the surface into a number of sectionsand provides a curved surface equation for each area as disclosed, forexample, in U.S. Pat. No. 5,886,766 incorporated herein in its entiretyby reference. Optimization of the surface may be carried out by anyconvenient method. Additional properties of a specific lens wearer maybe introduced into the design optimization process including, withoutlimitation, variations in the pupil diameter of about 1.5 to about 7 mm,image convergence at a point about 25 to about 28 mm behind the frontvertex of the surface, pantoscopic tilt of about 7 to about 20 degreesand the like, and combinations thereof.

The distance and near vision powers for the progressive addition surfacedesign u(x, y) are selected so that powers of the lens are those neededto correct the lens wearer's visual acuity. The dioptric add power willtypically be about +0.10 to

about +6.00 diopters. Generally, the distance curvature of theprogressive surface will be within about 0.25 to about 8.50 diopters.The near vision curvature will be about 1.00 to about 12.00 diopters.

In the second step of the method of the invention, the surface u(x,y) isexpressed as a plurality of sag values. This step may be carried out bysubtracting u(x,y) from the base spherical surface u_(o)(x, y), with acurvature equal to the distance curvature or base curvature, to yieldthe surface's sag values v(x,y). The coordinates of the point of maximumunwanted astigmatism x_(m),y_(m) on one side of the channel are located.

One ordinarily skilled in the art will recognize that, for theprogressive surface u(x,y), the principal curvatures c₁ and c₂ at anypoint x,y may be given by: $\begin{matrix}{c_{1} = {H + \left\lbrack {H^{2} - K} \right\rbrack^{1/2}}} & (I) \\{{c_{2} = {H - \left\lbrack {H^{2} - K} \right\rbrack^{1/2}}}{{where}\text{:}}} & ({II}) \\{{H = \frac{{\left( {1 + u_{x}^{2}} \right)u_{yy}} - {2u_{x}u_{y}u_{x,y}} + {\left( {1 + u_{y}^{2}} \right)u_{xx}}}{2\left( {1 + u_{x}^{2} + u_{y}^{2}} \right)^{3/2}}}{and}} & ({III}) \\{K = \frac{{u_{xx}u_{yy}} - u_{xy}^{2}}{\left( {1 + u_{x}^{2} + u_{y}^{2}} \right)^{2}}} & ({IV})\end{matrix}$wherein H is the Gaussian curvature; andK is the mean curvature.For the curvature, c, in a particular direction y, the above equationsreduce to: $\begin{matrix}{C = \frac{\frac{\partial^{2}u}{\partial y^{2}}}{\left( {1 + \left( \frac{\partial u}{\partial y} \right)^{2}} \right)^{3/2}}} & (V)\end{matrix}$For optical lenses, the dioptric power, P(x,y), and unwantedastigmatism, A(x,y), at a point on the lens at x,y are given by:P=(n−1)*[c ₁ +c ₂]/2  (VI)A=Abs[c ₁ −c ₂]  (VII)wherein n is the refractive index; andAbs stands for “absolute value.”

The coordinates of the maximum unwanted astigmatism may be defined asx_(m),y_(m) and are typically located on either side of the channel. Theequations may be used to reduce the magnitude of the unwantedastigmatism on a progressive surface while maintaining the requiredpower in the area. However, a result of this reduction will be that theastigmatism will increase at another location on the surface

due to a change in curvature at that location. Optimization techniqueshave been developed which include merit functions to specify where theastigmatism may be allowed to increase. One such technique is disclosedin U.S. Pat. No. 6,302,540. Such techniques generally are complicated,time consuming, and tend to impact the progressive surface on a globalrather than local scale compromising distance, reading, and channel zonewidths, channel length and the like. Thus, such methods are unsuited forproducing a progressive surface having areas of unwanted astigmatism inwhich the magnitude of astigmatism is low.

It is a discovery of the invention that the magnitude of unwantedastigmatism may be reduced in a local area, without increasing unwantedastigmatism at another location on the lens surface, by the followingmethod. In this method, the progressive surface u(x,y) is specified as zsag values at points s on an x-y grid. The grid spacing may be anyconvenient spacing, but preferably is between about 0.01 and 4 mm, morepreferably between about 0.1 and about 2 mm, and most preferably about0.5 to about 1 mm. The sag values v(x,y) in a local area that includes apoint (x_(m),y_(m)) of maximum unwanted astigmatism are selected for theoptimization method. This vicinity conveniently may be defined as anygeometric shape, but preferably is defined as a circle or morepreferably as a square centered at (x_(m),y_(m)). In cases in which asquare is used, a square centered around (x_(m),y_(m)) may be formedfrom a grid with a minimum number of 5 points to a maximum number of 81points. Preferably, 9 points arranged as a grid of 3×3 points is used.In cases in which a circle is used, preferably the circle's diameter isbetween about 1 and 10 mm, more preferably between about 3 and 6 mm,most preferably about 4 mm. The 4 mm circle is most preferred becausethe average pupil diameter projected on the lens surface isapproximately 4 mm at normal illumination conditions. If too large anarea is used, undesirable changes will result in other areas of thelens.

The sag values v(x, y) are approximated by a toric surface in the localarea centered around the unwanted astigmatism maximum. Using this localapproximation, the principal curvatures at x_(m), y_(m) are recalculatedusing Equations I and II. Adjustments are made in the sag values in thesurface v(x,y) in increments of between about 0.00001 mm and about 0.01mm, preferably about 0.0001 mm depending on the grid spacing selected,at grid points which lay closest to the periphery of the area until themaximum unwanted astigmatism shifts to another surface location that iswithin the area. More specifically, the sag value of each of the pointssurrounding (x_(m),y_(m)) may be sequentially increased by about 0.0001mm to determine if the astigmatism at (x_(m),y_(m)) decreases. If theastigmatism does not decrease, then the sag value of each of the pointsmay be sequentially decreased to determine if the astigmatism at(x_(m),y_(m)) decreases. Once the unwanted astigmatism at (x_(m),y_(m))decreases sufficiently to move the maximum to another point location(x′_(m),y′_(m)), the process at (x_(m),y_(m)) stops and is resumed atpoints surrounding (x′_(m), y′_(m)).

The process is then repeated until the unwanted astigmatism within thearea is substantially free of points at which the magnitude of themaximum astigmatism is at its original level. An area results in whichthe magnitude of the maximum astigmatism is substantially constant, forexample that the unwanted astigmatism has a peak height less than about0.1 diopters in a 5 mm diameter area. Additionally, the magnitude of themaximum astigmatism is reduced as compared to the maximum astigmatismoriginally found in the area. The process is then repeated for the areasof maximum, localized unwanted astigmatism on the opposite side of thechannel.

In an optional, and preferred, final step of the method of theinvention, the resulting surface is smoothed by any suitable fittingtechnique to eliminate any significant curvature discontinuities, ordiscontinuities that result in localized power changes of greater thanabout 0.05 diopters. Any known technique may be used including, withoutlimitation, fitting using polynomial, splines and the like.

The resulting optimized and smoothed surface will not changesubstantially from the first surface because the optimization isperformed locally in the areas of unwanted astigmatism. However, ifsignificant changes do occur, appropriate compensations in power may beincorporated into a complementary surface of the lens to offset thechanges. Accordingly, other surfaces designed to adapt the lens to theophthalmic prescription of the lens wearer may be used in combinationwith, or addition to, the optimized progressive addition surface.Additionally, the individual surfaces of the lens may have a sphericalor aspherical distance vision zone. The channel or corridor of visionfree of unwanted astigmatism, may be closer to the distance or nearviewing zone. Further, combinations of any of the above variations maybe used.

In a preferred embodiment, the lens of the invention has as its convexsurface the surface of the invention and a complementary concave surfacewhich concave surface corrects the wearer's astigmatism and prism. Theconvex surface preferably is of a symmetric, soft design produced bycombining two convex progressive surfaces. Both of the progressivesurfaces have a channel length of about 10 to about 22 mm. One surfacehas an aspherical distance viewing zone and the maximum, localizedunwanted astigmatism is located closer to the distance than the nearviewing zone preferably on either side of the upper two thirds of thechannel. The distance zone is aspherized to provide additional pluspower to the surface of up to about 2.00 diopters, preferably up toabout 1.00 diopters, more preferably up to about 0.50 diopters.Aspherization may be outside of a circle centered at the fitting pointhaving a radius of about 10 mm, preferably about 15 mm, more preferablyabout 20 mm. The other surface has no aspherical distance viewing zoneand the maximum, localized unwanted astigmatism is located closer to thenear viewing zone than the distance viewing zone, preferably on eitherside of the lower two thirds of the channel.

The lenses of the invention may be constructed of any known materialsuitable for production of ophthalmic lenses. Such materials may beconstructed of any known material suitable for production of ophthalmiclenses. Such materials are either commercially available or methods fortheir production are known. Further, the lenses may be produced by anyconventional lens fabrication technique including, without limitation,grinding, whole lens casting, molding, thermoforming, laminating,surface casting, or combinations thereof.

The invention will be clarified further by a consideration of thefollowing, non-limiting examples.

EXAMPLES Example 1

A contour map for a commercially available lens, Varilux COMFORT™,progressive addition lens was created using a coordinate measuringmachine and using the sag values obtained in a ray trace program toobtain power and cylinder profiles. The map is shown as FIG. 1 a. FIG. 1b shows the cylinder profile (A) and power profile (B) of across-sectional portion of the lens at the narrowest portion of thechannel. The lens, Lens 1, had a refractive index of 1.498, base curveof 95.1 mm and add power of 2.04 diopters. FIGS. 1 a and 1 b show thatthere is a noticeable maximum unwanted astigmatism on either side of thechannel. The unwanted astigmatism increases by 0.25 diopters over a 10mm diameter circle and the maximum unwanted astigmatism within this areais 2.64 diopters and located at x=8.2 mm and y=−10.7 mm. FIG. 2 a is acontour map created for Lens 2, a second commercially available lens,Sola PERCEPTA™, having a refractive index of 1.498, a base curve of 99.9mm and 2.10 diopter add power. FIGS. 2 a and 2 b show that there is anoticeable maximum unwanted astigmatism on either side of the channel.The unwanted astigmatism increases by 0.40 diopters over a 10 mmdiameter circle, the maximum unwanted astigmatism in this area for thesecond lens is 2.53 diopters at x=15.3 and y=−12.2 mm. FIG. 3 a is acontour map created

for a Lens 3, third commercial lens, DEFINITY™, having a refractiveindex of 1.51, a base curve of 106.2 mm and 2.04 diopter add power.FIGS. 3 a and 3 b show that there is a noticeable maximum unwantedastigmatism on either side of the channel. The unwanted astigmatismincreases by 0.25 diopters over a 10 mm diameter circle and the maximumunwanted astigmatism within this area is 1.64 diopters at x=12.5 mm andy=−12.3 mm.

Example 2

A convex progressive surface (A) was designed using a materialrefractive index of 1.586, base curve of 104.4 mm, and add power of 2.02diopters. This surface, Surface 1, had a noticeable maximum unwantedastigmatism on either side of the channel. The unwanted astigmatismincreases by 0.20 diopters over a 10 mm diameter circle, and the maximumunwanted astigmatism within this area is 1.36 diopters at x=8.8 mm andy=−7.4 mm. The prism reference point used was x=0 and y=0. FIG. 4 b isthe power and astigmatism profile of the surface across the narrowestcross-section of the channel. The profile shows a maximum in theunwanted astigmatism.

The surface produced by the above design methodology is a convexprogressive addition surface B made from a material refractive index of1.586, base curve of 103.7 mm and add power of 1.94 diopters. A gridspacing of 2 mm, a local area for the toric approximation of 9 pointsarranged as a 3×3 grid and increments of 0.0001 mm for sag changes wereused. FIG. 5 a depicts the unwanted astigmatism contours of Surface B.As listed on Table 1, the maximum, localized astigmatism was 1.17diopters at x=12.6 mm and y=−11.1. mm. The prism reference point was x=0and y=0. FIG. 5 b shows the power and astigmatism profiles acrossvarious cross-sections of the channel (denoted by their y coordinates).The profile shows that the unwanted astigmatism maxima are significantlyreduced in magnitude and are 0.10 diopters in a 10 mm diameter circle.TABLE 1 Optical Parameter Lens 1 Lens 2 Lens 3 Surface A Surface BDistance 0.01 −0.01 0.08 0.03 0.09 Power (D) Add Power (D) 2.04 2.102.04 2.02 1.94 Distance 7.9 14.2 13.5 12.4 9.7 Width (mm) Reading Width18.3 15.5 16.2 15.4 27.5 (mm) Reading Power 13.8 12.4 8.0 6.3 4.0 Width(mm) Channel 11.6 12.5 12.8 12.2 12.2 Length (mm) Channel Width 6.6 6.78.8 8.0 8.3 (mm) Max. Astig. 18.2, −10.7 15.3, −12.2 12.5, −12.3 8.8,−7.4 12.6, −11.1 Location (x, y in deg.) Max. Astig. 2.64 2.53 1.64 1.361.17 (D) Max Astig. 0.25 0.40 0.25 0.20 0.10 Amp. Per 10 mm Diameter (D)

1. A method for designing a progressive addition lens, comprising thesteps of: a.) designing a first progressive addition surface having achannel, and one or more areas of unwanted astigmatism on either side ofthe channel, each area of unwanted astigmatism comprising a maximumunwanted astigmatism; b.) expressing the first surface as a plurality ofsag values; and c.) modifying each of the one or more areas of unwantedastigmatism to provide a second progressive addition surface in whichthe maximum unwanted astigmatism of each of the areas is reduced andsubstantially constant throughout the area; wherein the modifying of afirst area of a first unwanted astigmatism is independent of a secondarea of a second unwanted astigmatism.
 2. The method of claim 1, furthercomprising d.) smoothing the second surface to eliminatediscontinuities.
 3. The method of claim 1, wherein step b.) furthercomprises expressing a surface u(x,y) as a plurality of sag values bysubtracting u(x,y) from a base spherical surface u_(o)(x, y) to yieldthe sag values.
 4. The method of claim 1, wherein step c.) furthercomprises: (i) specifying a surface u(x,y) as a plurality of sag valuesat points on an x-y grid; (ii) defining an area which area comprises apoint (^(X) _(m),^(Y) _(m)) of maximum unwanted astigmatism; (iii)approximating the sag values for the area using a toric surface; (iv)calculating principal curvatures at the point of maximum unwantedastigmatism; and (v) adjusting the sag values until the maximum unwantedastigmatism shifts to another surface location that is within the area;and (vi) repeating steps (iii) through (v) until the maximum unwantedastigmatism within the area is reduced and is substantially constantthroughout the area.
 5. The method of claim 4, wherein the areacomprises a square centered at (^(X) _(m),^(Y) _(m)).
 6. The method ofclaim 4, wherein the area comprises a circle centered at (X_(m)Y_(m)).7. The method of claim 6, wherein the circle is of a diameter of about 1to about 10 mm.
 8. The method of claim 6, wherein the diameter of thecircle is about 4 mm.
 9. The method of claim 1, wherein the lens is aspectacle lens. 10-11. (canceled)